Method for segmenting and denoising triangle mesh

ABSTRACT

A method for segmenting and denoising a triangle mesh, the method comprising: reading triangle mesh data containing N triangular patches, determining the noise level of the triangle mesh data, and optimizing data at a noise level higher than a preset value; segmenting the triangle mesh data by using a region growing segmentation algorithm, such that a plurality of sub-regions of the triangle mesh data are formed; optimizing the segmented triangle mesh data by using a hole-filling algorithm; and filtering the segmented triangle mesh data by using a denoising algorithm.

The present application claims priority to Chinese Patent ApplicationNo. 202010965873.1, filed on Sep. 15, 2020 with the China NationalIntellectual Property Administration, which is incorporated herein byreference in its entirety.

FIELD

The present disclosure relates to the technical field of imageprocessing, and in particular to a segmenting and denoising method basedon triangle meshes.

BACKGROUND

With the wide application of the three-dimensional scanning datatechnology in fields such as artificial intelligence devicemanufacturing, industrial detection, target identification and VR/AR,improving the quality of the scanned data is of great significance forthe development of the above fields. In related technology, the amountof initial point cloud data obtained through three-dimensional scanningis very large, and the amount of data to be stored is huge, so that itis difficult to perform algorithm processing. Therefore, it is usuallyrequired to perform surface reconstruction on initial data to obtain atriangular mesh model, so as to obtain simple and common data.

However, in the scanning and reconstruction processes, the triangularmesh model is inevitably contaminated by noise. Due to the noise, thedata quality of the triangular mesh model is to be reduced, andsubsequent mesh processing is to be affected, thereby affecting theeffect of three-dimensional scanned images. The denoising methods andtechnologies in the conventional technology have at least the followingthree problems. (1) According to most of the triangular mesh denoisingmethods in the conventional technology, local neighborhood informationis used. In performing denoising, isotropic points or surfaces in aneighborhood are assigned larger weights, and anisotropic points orsurfaces in the neighborhood are assigned smaller weights. However, thesmaller weights still affect the denoising effect, resulting indestroying the sharp feature to some extent. (2) In order to suppressthe influence of the anisotropic points or faces on the denoisingeffect, parameters such as an angle and a distance are introduced inperforming denoising, increasing the difficulty of parameter tuning.Moreover, it is difficult to achieve an expected effect in this way,especially for those skilled in the art that are not familiar withalgorithms, which often increases their burden. (3) In other methodsaccording to the conventional technology, mesh denoising is performedbased on more information, resulting in a large amount of computationand slow speed.

SUMMARY

A segmenting and denoising method based on triangle meshes is providedaccording to the present disclosure, effectively segmenting a model withnoise, improving the speed of processing noise, and effectivelypreserving boundary features and details of data.

A segmenting and denoising method based on triangle meshes is providedaccording to an embodiment. The method includes: reading triangle meshdata including N triangular patches, determining a noise level of thetriangle mesh data, and optimizing triangle mesh data having a noiselevel greater than a predetermined threshold where N is greater thanone; segmenting the triangle mesh data by using a region growingsegmentation algorithm to form multiple sub-regions; optimizing thesegmented triangle mesh data by using a hole-filling algorithm; andfiltering the segmented triangle mesh data by using a denoisingalgorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of a segmenting and denoising method based ontriangle meshes according to an embodiment of the present disclosure;

FIG. 2 is a schematic structural diagram of two triangles sharing a sameside according to an embodiment of the present disclosure;

FIG. 3 is a schematic diagram showing an effect of segmenting trianglemesh data to form multiple sub-regions according to an embodiment of thepresent disclosure;

FIG. 4 is a schematic diagram showing an effect of segmenting a modelwith a small noise according to an embodiment of the present disclosure;

FIG. 5 is a schematic diagram showing effects of segmenting a model witha small noise at different D_(thr) according to an embodiment of thepresent disclosure;

FIG. 6 is a schematic diagram showing an effect of marking an edge,having a noise level greater than a predetermined D_(thr), of a modelwith a small noise at the D_(thr) according to an embodiment of thepresent disclosure;

FIG. 7 is a schematic diagram showing segmenting a model with a largenoise and marking the segmented model with the large noise to theoriginal model with the large noise according to an embodiment of thepresent disclosure;

FIG. 8 is a schematic diagram showing an effect of denoising a modelwith a large noise according to an embodiment of the present disclosure;

FIG. 9 is a schematic diagram showing an effect of denoising a modelwith a large noise according to another embodiment of the presentdisclosure;

FIG. 10 is a schematic diagram showing an effect of denoising a modelwith a small noise according to an embodiment of the present disclosure;

FIG. 11 is a schematic diagram showing an effect of denoising a modelwith a small noise according to another embodiment of the presentdisclosure;

FIG. 12 is a schematic diagram showing an effect of denoising a modelwith a small noise with different Gaussian space filtering kernelsaccording to an embodiment of the present disclosure; and

FIG. 13 is a schematic diagram showing results of denoising a model witha small noise with a hole-filling algorithm and without a hole-fillingalgorithm according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the description of the present disclosure, it should be understoodthat the orientation or positional relationship indicated by the terms,such as “up”, “low”, “front”, “back”, “left”, “right” and “horizontal”,are based on the orientation or positional relationship shown in thedrawings, which are only for facilitating the description of the presentdisclosure and simplifying the description, rather than indicating orimplying that the device or element referred to must have a specificorientation, and be constructed and operated in a particularorientation. Therefore, the above terms should not be understood as alimitation to the present disclosure.

In the description of the present disclosure, terms such as“installation”, “link”, “connection” and “fix” should be understoodbroadly, unless otherwise specifically defined. For example, it may be afixed connection, a detachable connection, or an integral connection; itmay be a mechanical connection or an electrical connection; and it maybe a direct connection, an indirect connection through an intermediatemedium, or an internal connection between two components. Those skilledin the art should understand specific meanings of the above terms in thepresent disclosure based on specific situations.

The present disclosure is further described in detail with reference toFIG. 1 to FIG. 12 and embodiments. However, the present disclosure isnot limited to the Figures and the embodiments.

A segmenting and denoising method based on triangle meshes is providedaccording to the present disclosure. The method includes the followingsteps S1 to S4.

In step S1, triangle mesh data including N triangular patches is read,where N is greater than one. A noise level of the triangle mesh data isdetermined. Triangle mesh data, having a noise level δ greater than orequal to 0.3 le, is optimized, where le is a noise level unit. Fortriangle mesh data having a noise level less than 0.3 le, proceed tostep S2.

For example, in a case that the read triangular mesh data only includesa Gaussian noise, it can be seen that based on a probability densityfunction

${p(z)} = {\frac{1}{\sqrt{2\pi\sigma}}{\exp( {- \frac{( {z - µ} )^{2}}{2\sigma^{2}}} )}}$

of the Gaussian noise, a Gaussian noise having a σ greater than or equalto 0.3 is defined as a large noise, where z represents coordinates ofthe triangular mesh, u represents an average of local coordinates of thetriangular mesh, and a represents a standard deviation.

In step S1, the data having a large noise level is optimized byconstructing an objective optimization function to enhance boundaryinformation of the data and facilitate segmenting the data. Theobjective optimization function may be expressed as:

min Σ_(i) ∥{tilde over (p)} _(i) −p _(i)∥₂ ²+αΣ_(e) w(e)∥D(e)∥₂ ²+βΣ_(e)w(e)∥R(e)∥₂ ².

There are some side-sharing triangles among the multiple triangularpatches. {tilde over (p)}_(i) represents an i-th vertex that has beenoptimized, p_(i) represents an i-th vertex that has not been optimized,∥{tilde over (p)}_(i)−p_(i)∥₂ ² represents a second norm of the vertex{tilde over (p)}_(i) and the vertex p_(i), α and β represent weightcoefficients, w(e) represents a weight distribution function of a sidebased on a normal, ∥D(e)∥₂ ² represents a second norm of a differentialedge operator D(e) of each of side-sharing triangles, R(e) represents aconstraint coefficient of a triangular patch, and ∥R(e)∥₂ ² represents asecond norm of the constraint coefficient R(e) of the triangular patch.As shown in FIG. 2 , in a case that four vertices of two side-sharingtriangles are represented by p1, p2, p3, and p4, R(e)=(p1−p2=p3−p4)².Therefore, shapes of the triangle patches are effectively optimized,avoiding spikes in the data and flipped triangular patches.

In step S2, the triangle mesh data is segmented by using a regiongrowing segmentation algorithm to form multiple sub-regions.

According to the conventional region growing algorithm, diffusion isusually performed based on a position relationship, and a normal orconnection information may be used as a condition for determining agrowing boundary. However, for a model with a noise, the determinationbased on a normal is easily affected by the noise. Therefore, in thesolution according to the present disclosure, a predetermined thresholdD_(thr) is set as a segmentation intensity coefficient and as acondition for determining a growing boundary. In a case that twoside-sharing triangles are coplanar, an L2 norm (modulus length) of thedifferential edge operator D(e) of the two side-sharing triangles isequal to zero. The L2 norm refers to a square root of a sum of squaresof all elements of a vector. Therefore, boundary features may beextracted by calculating the modulus length of the differential edgeoperator.

According to the present disclosure, in the segmentation by using theregion growing segmentation algorithm, a feature and a signal of acurrent region are concentrated, effectively reducing the influence ofsignals from different regions. In addition, compared with theconventional technology, in the optimization process according to thepresent disclosure, the data with a noise is segmented and then isfiltered, and denoising processing is performed on each of sub-regionsobtained by performing region segmenting, effectively preservingboundary features and details. Furthermore, with the technical solutionsaccording to the present disclosure, the stability of the algorithms issignificantly improved, and a good optimization effect can be achievedin segmenting a model with a nose.

In step S2-1, a triangular patch is selected from the triangle meshdata, side-sharing triangles of the triangular patch are traversed, anda differential edge operator D(e) for each of the side-sharing trianglesis calculated.

In step S2-2, the threshold D_(thr) is determined as a condition fordetermining a region growing boundary. For each of the side-sharingtriangles, a norm ∥D(e)∥ is calculated. A side-sharing triangle, havinga norm ∥D(e)∥ less than D_(thr), of the triangular patch is grouped intoa same sub-region as the triangular patch.

As shown in FIG. 3 , F1 represents a seed patch that has not beensegmented. Each of side-sharing triangles of the seed patch istraversed. For each of the side-sharing triangles of the seed patch, itis determined whether a norm ∥D(e)∥ of the side-sharing triangle is lessthan D_(thr), and the side-sharing triangle is marked as a new seedpatch F2 in a case that norm ∥D(e)∥ of the side-sharing triangle is lessthan D_(thr). Then, diffusion and clustering are continuously performeduntil norms ∥D(e)∥ of all new seed patches are greater than D_(thr).

In addition, due to the noise, after the triangular mesh model issegmented into multiple sub-regions in step S2, there may be some local“small region” meshes that are incorrectly segmented, which seriouslyaffect the denoising effect. With a hole-filling algorithm, refinementand optimization are performed, thereby obtaining an accuratesegmentation result.

In step S3, the segmented triangle mesh data is optimized by using ahole-filling algorithm.

In step S3-1, the multiple sub-regions are retrieved to obtain ato-be-corrected triangle.

In step S3-2, a second-order neighborhood S(i) of each of theto-be-corrected triangle is traversed.

In step S3-3, for each of the to-be-corrected triangle, a normal n_(i)of the to-be-corrected triangle is determined, a normal n_(j) of atriangle in each of regions in the second-order neighborhood S(i) isdetermined, and the n_(i) and the n_(j) are accumulated. The n_(i) andthe n_(j) are accumulated by using the following equation:

$A = {\arg\max{\sum\limits_{j \in {S(i)}}{\cos( {n_{i},n_{j}} )}}}$

where A represents a sum obtained by accumulating a cosine value of then_(i) and a cosine value of the n_(j), and cos(n_(i), n_(j)) representsthe cosine value of the n_(i) and the cosine value of the n_(j).

In addition, the segmentation process in the present disclosure may beembedded in a denoising algorithm for all local points or planes, whichhas strong versatility and excellent operation performance.

In step S4, the segmented triangle mesh data may be filtered by using afast normal filtering algorithm, a bilateral normal filtering algorithm,a guide normal filtering algorithm, or an L1 median filtering algorithmto obtain required images.

For the fast normal filtering algorithm, the filtering process includes:performing weighted averaging on a normal of adjacent patches,eliminating an interfering patch by using a threshold, iterativelyfiltering a normal of a patch with a noise, and iteratively updatingpositions of vertices to match the denoised normal of the patch. Thus,an image is filtered.

For the bilateral normal filtering algorithm, the filtering processincludes: iteratively updating a normal domain by using a spatialdistance weight, a method weight and a bilateral operator, and theniteratively updating positions of vertices. Thus, an image is filtered.

For the guide normal filtering algorithm, the filtering processincludes: performing joint bilateral filtering on a normal of atriangular patch, and updating positions of vertices based on thefiltered normal. Thus, an image is filtered. In addition, in performingjoint bilateral filtering on the normal of the triangular patch, anappropriate guiding normal should be selected.

In the L1 median filtering algorithm, the filtering process includes:preprocessing an inputted mesh with a noise, estimating a normal of adenoised patch by using an L1 median filter, and iteratively updatingpositions of vertices. Thus, an image is filtered.

For each of the side-sharing triangles, the differential edge operatorD(e) is calculated by using the following equation:

${D(e)} = {\begin{bmatrix}\frac{{{\Delta_{1,2,3}( {p_{4} - p_{3}} )} \cdot ( {p_{3} - p_{1}} )} + {{\Delta_{1,3,4}( {p_{1} - p_{3}} )} \cdot ( {p_{3} - p_{2}} )}}{( {❘{p_{3} - p_{1}}❘} )^{2}( {\Delta_{1,2,3} + \Delta_{1,3,4}} )} \\\frac{\Delta_{1,3,4}}{\Delta_{1,2,3} + \Delta_{1,3,4}} \\\frac{{{\Delta_{1,2,3}( {p_{3} - p_{1}} )} \cdot ( {p_{1} - p_{4}} )} + {{\Delta_{1,3,4}( {p_{2} - p_{1}} )} \cdot ( {p_{1} - p_{3}} )}}{( {❘{p_{3} - p_{1}}❘} )^{2}( {\Delta_{1,2,3} + \Delta_{1,3,4}} )} \\\frac{\Delta_{1,2,3}}{\Delta_{1,2,3} + \Delta_{1,3,4}}\end{bmatrix}^{T}\begin{bmatrix}p_{1} \\p_{2} \\p_{3} \\p_{4}\end{bmatrix}}$

where p₁, p₂, p₃, and p₄ represent four vertices of two trianglessharing a same side; in a three-dimensional rectangular coordinatesystem, coordinates of p₁ are expressed as (x₁, y₁, z₁), coordinates ofp₂ are expressed as (x₂, y₂, z₂), coordinates of p₃ are expressed as(x₃, y₃, z₃), coordinates of p₄ are expressed as (x₄, y₄, z₄), p₁-p₃represents (x₁, y₁, z₁)-(x₃, y₃, z₃), p₁-p₄ represents (x₁, y₁, z₁)-(x₄,y₄, z₄), p₃-p₁ represents (x₃, y₃, z₃)-(x₁, y₁, z₁). p₂-p₁ represents(x₂, y₂, z₂)-(x₁, y₁, z₁), p₃-p₂ represents (x₃, y₃, z₃)-(x₂, y₂, z₂),and p₄-p₃ represents (x₄, y₄, z₄)-(x₃, y₃, z₃); Δ_(1,2,3) represents anarea of a triangle defined by p₁, p₂ and p₃, and Δ_(1,3,4) represents anarea of a triangle defined by p₁, p₃ and p₄.

The norm ∥D(e)∥ is calculated by using the following equation:

∥D(e)∥=√{square root over (D(e)_(x) ² +D(e)_(y) ² +D(e)_(z) ²)}

where D(e)_(x) represents a differential edge operator for aside-sharing triangle in an x direction of a three-dimensionalrectangular coordinate system, D(e)_(y) represents a differential edgeoperator for a side-sharing triangle in a y direction of thethree-dimensional rectangular coordinate system, and D(e)_(z) representsa differential edge operator for a side-sharing triangle in a zdirection of the three-dimensional rectangular coordinate system.

As shown in FIG. 4 and FIG. 5 , a model with a noise level δ equal to0.2 le is segmented by performing the operations described in the abovestep S2. The segmentation effect varies with the segmentation intensitycoefficient D_(thr). It can be seen from FIG. 6 that a boundary of themodel may be determined and extracted by comparing ∥D(e)∥ with D_(thr),facilitating subsequent denoising processing.

As shown in FIG. 7 , a model with a large noise having a noise level δequal to 0.4 le is taken as an example. The model is optimized, then issegmented, and then is refined by using a region hole-filling algorithm,and finally is marked to the original model.

As shown in FIG. 8 , a cube-shape model with a noise level δ equal to0.8 le is taken as an example. The noise level of the model is toolarge, so that the model is preprocessed to enhance boundaryinformation. Then, the model is segmented. The segmentation andclustering are marked to the original model. Then, denoising isperformed. In FIG. 8 , UNF represents the fast normal filteringalgorithm, BNF represents the bilateral normal filtering algorithm, andGNF represents the guide normal filtering algorithm. The upper row inFIG. 8 shows a denoising effect by using the denoising methods accordingto the conventional technology. The upper row in FIG. 8 , from left toright, shows an original model, a model obtained with the bilateralnormal filtering algorithm, a model obtained with the fast normalfiltering algorithm, a model obtained with the guide normal filteringalgorithm, and a model obtained with the L1 median filtering algorithm.The lower row in FIG. 8 shows a denoising effect by using the denoisingmethod based on a segmentation framework according to the presentdisclosure. The lower row in FIG. 8 , from left to right, shows anoriginal model marked with a segmentation result, a model obtained byperforming segmentation and then filtering by using the bilateral normalfiltering algorithm, a model obtained by performing segmentation andthen filtering by using the fast normal filtering algorithm, a modelobtained by performing segmentation and then filtering by using theguide normal filtering algorithm, and a model obtained by performingsegmentation and then filtering by using the L1 median filteringalgorithm. It is apparent that the optimization effect of the imageobtained by using the method according to the present disclosure isbetter.

As shown in FIG. 9 , a vase model with a noise level δ equal to 0.5 leis taken as an example. By comparing the upper row and the lower row inFIG. 9 , it can be seen that the denoising method based on asegmentation framework has a better denoising effect. The Englishletters in FIG. 9 represent the same meaning as the English letters inFIG. 8 .

As shown in FIG. 10 , a fandiah model with a noise level δ equal to 0.1le is taken as an example. By comparing the upper row and the lower rowin FIG. 10 , it can be seen that the denoising method based on asegmentation framework has a better denoising effect. The Englishletters in FIG. 10 represent the same meaning as the English letters inFIG. 8 .

As shown in FIG. 11 , a dodecahedron model with a noise level δ equal to0.2 le is taken as an example. By comparing the upper row and the lowerrow in FIG. 11 , it can be seen that the denoising method based on asegmentation framework has a better denoising effect. The Englishletters in FIG. 11 represent the same meaning as the English letters inFIG. 8 .

As shown in FIG. 12 , a dodecahedron model with a noise level δ equal to0.2 le is taken as an example. By comparing the upper row and the lowerrow in FIG. 12 , it can be seen that in a case of performing the guidenormal filtering algorithm, for different Gaussian space filteringkernels λr, a denoising effect of the denoising method based on asegmentation framework is less affected by the parameter λr, and thedenoising method based on a segmentation framework has a betteroptimization effect.

As shown in FIG. 13 , an octahedron model with a noise level δ equal to0.1 le is taken as an example. A denoising result with the hole-fillingalgorithm and a denoising result without the hole-filling algorithm arecompared. The diagram (a) in FIG. 13 shows a clustering result withoutthe hole-filling algorithm. The diagram (b) in FIG. 13 shows a resultobtained by performing denoising based on the clustering result withoutthe hole-filling algorithm as shown in diagram (a). The diagram (c) inFIG. 13 shows a result obtained by performing clustering optimizationbased on the result as shown in diagram (b) with the hole-fillingalgorithm. The diagram (d) in FIG. 13 shows a result obtained byperforming denoising based on the result as shown in diagram (c). It canbe seen from the diagrams in FIG. 13 that a denoising effect with thehole-filling algorithm is better.

The segmentation algorithm in the present disclosure is performed forsubsequent denoising algorithm. With the segmentation algorithm, aframework for enhancing the triangular mesh denoising algorithm in theconventional technology is provided, thereby improving the performanceof the denoising algorithm. In addition, some denoising algorithms areembedded in the segmented model according to the present disclosure,avoiding the influence of a non-heterogeneous neighborhood on thedenoising result, improving the operational performance, therebyeffectively and significantly enhancing the protection of the sharpfeatures.

1. A segmenting and denoising method based on triangle meshes,comprising: reading triangle mesh data comprising N triangular patches,determining a noise level of the triangle mesh data, and optimizingtriangle mesh data having a noise level greater than a predeterminedthreshold, wherein N is greater than one; segmenting the triangle meshdata by using a region growing segmentation algorithm to form aplurality of sub-regions; optimizing the segmented triangle mesh data byusing a hole-filling algorithm; and filtering the segmented trianglemesh data by using a denoising algorithm.
 2. The segmenting anddenoising method based on triangle meshes according to claim 1, whereinthe segmenting the triangle mesh data by using a region growingsegmentation algorithm to form a plurality of sub-regions comprises:selecting a triangular patch of the triangle mesh data, traversing eachof side-sharing triangles of the triangular patch, and calculating adifferential edge operator D(e) for each of the side-sharing trianglesof the triangular patch; and determining a threshold D_(thr) as acondition for determining a region growing boundary, calculating a norm∥D(e)∥ for each of the side-sharing triangles of the triangular patch,and grouping a side-sharing triangle, having a norm ∥D(e)∥ less thanD_(thr), of the triangular patch into a same sub-region as thetriangular patch.
 3. The segmenting and denoising method based ontriangle meshes according to claim 2, wherein for each of theside-sharing triangles, the differential edge operator D(e) iscalculated by using the following equation: ${D(e)} = {\begin{bmatrix}\frac{{{\Delta_{1,2,3}( {p_{4} - p_{3}} )} \cdot ( {p_{3} - p_{1}} )} + {{\Delta_{1,3,4}( {p_{1} - p_{3}} )} \cdot ( {p_{3} - p_{2}} )}}{( {❘{p_{3} - p_{1}}❘} )^{2}( {\Delta_{1,2,3} + \Delta_{1,3,4}} )} \\\frac{\Delta_{1,3,4}}{\Delta_{1,2,3} + \Delta_{1,3,4}} \\\frac{{{\Delta_{1,2,3}( {p_{3} - p_{1}} )} \cdot ( {p_{1} - p_{4}} )} + {{\Delta_{1,3,4}( {p_{2} - p_{1}} )} \cdot ( {p_{1} - p_{3}} )}}{( {❘{p_{3} - p_{1}}❘} )^{2}( {\Delta_{1,2,3} + \Delta_{1,3,4}} )} \\\frac{\Delta_{1,2,3}}{\Delta_{1,2,3} + \Delta_{1,3,4}}\end{bmatrix}^{T}\begin{bmatrix}p_{1} \\p_{2} \\p_{3} \\p_{4}\end{bmatrix}}$ where p₁, p₂, p₃, and p₄ represent four vertices of twotriangles sharing a same side; in a three-dimensional rectangularcoordinate system, coordinates of p₁ are expressed as (x₁, y₁, z₁),coordinates of p₂ are expressed as (x₂, y₂, z₂), coordinates of p₃ areexpressed as (x₃, y₃, z₃), coordinates of p₄ are expressed as (x₄, y₄,z₄), p₁-p₃ represents (x₁, y₁, z₁)-(x₃, y₃, z₃), p₁-p₄ represents (x₁,y₁, z₁)-(x₄, y₄, z₄), p₃-p₁ represents (x₃, y₃, z₃)-(x₁, y₁, z₁). p₂-p₁represents (x₂, y₂, z₂)-(x₁, y₁, z₁), p₃-p₂ represents (x₃, y₃, z₃)-(x₂,y₂, z₂), and p₄-p₃ represents (x₄, y₄, z₄)-(x₃, y₃, z₃); Δ_(1,2,3)represents an area of a triangle defined by p₁, p₂ and p₃, and Δ_(1,3,4)represents an area of a triangle defined by p₁, p₃ and p₄.
 4. Thesegmenting and denoising method based on triangle meshes according toclaim 2, wherein the norm ∥D(e)∥ is calculated by using the followingequation:∥D(e)∥=√{square root over (D(e)_(x) ² +D(e)_(y) ² +D(e)_(z) ²)} whereD(e)_(x) represents a differential edge operator for a side-sharingtriangle in an x direction of a three-dimensional rectangular coordinatesystem, D(e)_(y) represents a differential edge operator for aside-sharing triangle in a y direction of the three-dimensionalrectangular coordinate system, and D(e)_(z) represents a differentialedge operator for a side-sharing triangle in a z direction of thethree-dimensional rectangular coordinate system.
 5. The segmenting anddenoising method based on triangle meshes according to claim 1, whereinthe optimizing the segmented triangle mesh data by using a hole-fillingalgorithm comprises: retrieving the plurality of sub-regions to obtain ato-be-corrected triangle; traversing a second-order neighborhood S(i) ofthe to-be-corrected triangle; and determining a normal n_(i) of theto-be-corrected triangle, determining a normal n_(j) of a triangle ineach of regions in the second-order neighborhood S(i), and accumulatingthe n_(i) and the n_(j).
 6. The segmenting and denoising method based ontriangle meshes according to claim 5, wherein the n_(i) and the n_(j)are accumulated by using the following equation:$A = {\arg\max{\sum\limits_{j \in {S(i)}}{\cos( {n_{i},n_{j}} )}}}$where A represents a sum obtained by accumulating a cosine value of then_(i) and a cosine value of the n_(j), and cos(n_(i), n_(j)) representsthe cosine value of the n_(i) and the cosine value of the n_(j).
 7. Thesegmenting and denoising method based on triangle meshes according toclaim 1, wherein triangle mesh data, having a noise level δ greater thanor equal to 0.3 le, is optimized, and le is a noise level unit.
 8. Thesegmenting and denoising method based on triangle meshes according toclaim 1, wherein the filtering the segmented triangle mesh data by usinga denoising algorithm comprises: filtering the segmented triangle meshdata by using a fast normal filtering algorithm, a bilateral normalfiltering algorithm, a guide normal filtering algorithm, and an L1median filtering algorithm.